1 // Copyright 2016 Ismael Jimenez Martinez. All rights reserved.
2 //
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
6 //
7 // http://www.apache.org/licenses/LICENSE-2.0
8 //
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
14
15 // Source project : https://github.com/ismaelJimenez/cpp.leastsq
16 // Adapted to be used with google benchmark
17
18 #include "benchmark/benchmark.h"
19
20 #include <algorithm>
21 #include <cmath>
22 #include "check.h"
23 #include "complexity.h"
24
25 namespace benchmark {
26
27 // Internal function to calculate the different scalability forms
FittingCurve(BigO complexity)28 BigOFunc* FittingCurve(BigO complexity) {
29 switch (complexity) {
30 case oN:
31 return [](int n) -> double { return n; };
32 case oNSquared:
33 return [](int n) -> double { return std::pow(n, 2); };
34 case oNCubed:
35 return [](int n) -> double { return std::pow(n, 3); };
36 case oLogN:
37 return [](int n) { return log2(n); };
38 case oNLogN:
39 return [](int n) { return n * log2(n); };
40 case o1:
41 default:
42 return [](int) { return 1.0; };
43 }
44 }
45
46 // Function to return an string for the calculated complexity
GetBigOString(BigO complexity)47 std::string GetBigOString(BigO complexity) {
48 switch (complexity) {
49 case oN:
50 return "N";
51 case oNSquared:
52 return "N^2";
53 case oNCubed:
54 return "N^3";
55 case oLogN:
56 return "lgN";
57 case oNLogN:
58 return "NlgN";
59 case o1:
60 return "(1)";
61 default:
62 return "f(N)";
63 }
64 }
65
66 // Find the coefficient for the high-order term in the running time, by
67 // minimizing the sum of squares of relative error, for the fitting curve
68 // given by the lambda expresion.
69 // - n : Vector containing the size of the benchmark tests.
70 // - time : Vector containing the times for the benchmark tests.
71 // - fitting_curve : lambda expresion (e.g. [](int n) {return n; };).
72
73 // For a deeper explanation on the algorithm logic, look the README file at
74 // http://github.com/ismaelJimenez/Minimal-Cpp-Least-Squared-Fit
75
MinimalLeastSq(const std::vector<int> & n,const std::vector<double> & time,BigOFunc * fitting_curve)76 LeastSq MinimalLeastSq(const std::vector<int>& n,
77 const std::vector<double>& time,
78 BigOFunc* fitting_curve) {
79 double sigma_gn = 0.0;
80 double sigma_gn_squared = 0.0;
81 double sigma_time = 0.0;
82 double sigma_time_gn = 0.0;
83
84 // Calculate least square fitting parameter
85 for (size_t i = 0; i < n.size(); ++i) {
86 double gn_i = fitting_curve(n[i]);
87 sigma_gn += gn_i;
88 sigma_gn_squared += gn_i * gn_i;
89 sigma_time += time[i];
90 sigma_time_gn += time[i] * gn_i;
91 }
92
93 LeastSq result;
94 result.complexity = oLambda;
95
96 // Calculate complexity.
97 result.coef = sigma_time_gn / sigma_gn_squared;
98
99 // Calculate RMS
100 double rms = 0.0;
101 for (size_t i = 0; i < n.size(); ++i) {
102 double fit = result.coef * fitting_curve(n[i]);
103 rms += pow((time[i] - fit), 2);
104 }
105
106 // Normalized RMS by the mean of the observed values
107 double mean = sigma_time / n.size();
108 result.rms = sqrt(rms / n.size()) / mean;
109
110 return result;
111 }
112
113 // Find the coefficient for the high-order term in the running time, by
114 // minimizing the sum of squares of relative error.
115 // - n : Vector containing the size of the benchmark tests.
116 // - time : Vector containing the times for the benchmark tests.
117 // - complexity : If different than oAuto, the fitting curve will stick to
118 // this one. If it is oAuto, it will be calculated the best
119 // fitting curve.
MinimalLeastSq(const std::vector<int> & n,const std::vector<double> & time,const BigO complexity)120 LeastSq MinimalLeastSq(const std::vector<int>& n,
121 const std::vector<double>& time, const BigO complexity) {
122 CHECK_EQ(n.size(), time.size());
123 CHECK_GE(n.size(), 2); // Do not compute fitting curve is less than two
124 // benchmark runs are given
125 CHECK_NE(complexity, oNone);
126
127 LeastSq best_fit;
128
129 if (complexity == oAuto) {
130 std::vector<BigO> fit_curves = {oLogN, oN, oNLogN, oNSquared, oNCubed};
131
132 // Take o1 as default best fitting curve
133 best_fit = MinimalLeastSq(n, time, FittingCurve(o1));
134 best_fit.complexity = o1;
135
136 // Compute all possible fitting curves and stick to the best one
137 for (const auto& fit : fit_curves) {
138 LeastSq current_fit = MinimalLeastSq(n, time, FittingCurve(fit));
139 if (current_fit.rms < best_fit.rms) {
140 best_fit = current_fit;
141 best_fit.complexity = fit;
142 }
143 }
144 } else {
145 best_fit = MinimalLeastSq(n, time, FittingCurve(complexity));
146 best_fit.complexity = complexity;
147 }
148
149 return best_fit;
150 }
151
ComputeBigO(const std::vector<BenchmarkReporter::Run> & reports)152 std::vector<BenchmarkReporter::Run> ComputeBigO(
153 const std::vector<BenchmarkReporter::Run>& reports) {
154 typedef BenchmarkReporter::Run Run;
155 std::vector<Run> results;
156
157 if (reports.size() < 2) return results;
158
159 // Accumulators.
160 std::vector<int> n;
161 std::vector<double> real_time;
162 std::vector<double> cpu_time;
163
164 // Populate the accumulators.
165 for (const Run& run : reports) {
166 CHECK_GT(run.complexity_n, 0) << "Did you forget to call SetComplexityN?";
167 n.push_back(run.complexity_n);
168 real_time.push_back(run.real_accumulated_time / run.iterations);
169 cpu_time.push_back(run.cpu_accumulated_time / run.iterations);
170 }
171
172 LeastSq result_cpu;
173 LeastSq result_real;
174
175 if (reports[0].complexity == oLambda) {
176 result_cpu = MinimalLeastSq(n, cpu_time, reports[0].complexity_lambda);
177 result_real = MinimalLeastSq(n, real_time, reports[0].complexity_lambda);
178 } else {
179 result_cpu = MinimalLeastSq(n, cpu_time, reports[0].complexity);
180 result_real = MinimalLeastSq(n, real_time, result_cpu.complexity);
181 }
182 std::string benchmark_name =
183 reports[0].benchmark_name.substr(0, reports[0].benchmark_name.find('/'));
184
185 // Get the data from the accumulator to BenchmarkReporter::Run's.
186 Run big_o;
187 big_o.benchmark_name = benchmark_name + "_BigO";
188 big_o.iterations = 0;
189 big_o.real_accumulated_time = result_real.coef;
190 big_o.cpu_accumulated_time = result_cpu.coef;
191 big_o.report_big_o = true;
192 big_o.complexity = result_cpu.complexity;
193
194 // All the time results are reported after being multiplied by the
195 // time unit multiplier. But since RMS is a relative quantity it
196 // should not be multiplied at all. So, here, we _divide_ it by the
197 // multiplier so that when it is multiplied later the result is the
198 // correct one.
199 double multiplier = GetTimeUnitMultiplier(reports[0].time_unit);
200
201 // Only add label to mean/stddev if it is same for all runs
202 Run rms;
203 big_o.report_label = reports[0].report_label;
204 rms.benchmark_name = benchmark_name + "_RMS";
205 rms.report_label = big_o.report_label;
206 rms.iterations = 0;
207 rms.real_accumulated_time = result_real.rms / multiplier;
208 rms.cpu_accumulated_time = result_cpu.rms / multiplier;
209 rms.report_rms = true;
210 rms.complexity = result_cpu.complexity;
211 // don't forget to keep the time unit, or we won't be able to
212 // recover the correct value.
213 rms.time_unit = reports[0].time_unit;
214
215 results.push_back(big_o);
216 results.push_back(rms);
217 return results;
218 }
219
220 } // end namespace benchmark
221